Question

Use
a slope field plotter to plot the slope field for the differential
equation

dy/dx=sqrt(x-y)

and plot the solution curve for the initial condition
y(2)=2

Answer #1

The slope field of the given differential equation is given in the below diagram.

The solution curve is also ploted by the red curve.

1. Sketch the direction field for the following differential
equation dy dx = y − x. You may use maple and attach your graph.
Also sketch the solution curves with initial conditions y(0) = −1
and y(0) = 1.

Solve the Homogeneous differential equation
(7 y^2 + 1 xy)dx - 1 x^2 dy = 0
(a) A one-parameter family of solution of the equation is y(x)
=
(b) The particular solution of the equation subject to the
initial condition y(1) =1/7.

Find the solution to the separable differential equation dy =
x cos2 y + sin x cos2 y satisfying π dx
the initial condition y = 4 when x = π.

Solve the given differential equation
y-x(dy/dx)=3-2x2(dy/dx)

A Bernoulli differential equation is one of the form
dy/dx+P(x)y=Q(x)y^n (∗)
Observe that, if n=0 or 1, the Bernoulli equation is linear. For
other values of n, the substitution u=y^(1−n) transforms the
Bernoulli equation into the linear equation
du/dx+(1−n)P(x)u=(1−n)Q(x).
Consider the initial value problem xy′+y=−8xy^2, y(1)=−1.
(a) This differential equation can be written in the form (∗)
with P(x)=_____, Q(x)=_____, and n=_____.
(b) The substitution u=_____ will transform it into the linear
equation du/dx+______u=_____.
(c) Using the substitution in part...

(x-y)dx + (y+x)dy =0 Solve the differential equation

1) Solve the given differential equation by separation of
variables.
exy
dy/dx = e−y +
e−6x −
y
2) Solve the given differential
equation by separation of variables.
y ln(x) dx/dy = (y+1/x)^2
3) Find an explicit solution of the given initial-value
problem.
dx/dt = 7(x2 + 1), x( π/4)= 1

dy/dx = x^4/y^2
a) use eulers method to approximate the solution at x =1.6
starting at the initial condition of y(1)=1 and a step size of
delta x=0.2
b) solve this differential equation exactly using separation
if variables and the inital condition y(1)=1
c) what is the exact vwlue of y(1.6) for the solution found in
part b

Find the general solution of the given differential equation
(x+!) dy/dx + (x+2)y = 2xe^-x
y = ______
Determine whether there are any transient terms in the general
solution.

exact differential equation, (2xy+x)dx+(x^2+y)dy=0

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